I have 3 Gmail accounts. I have created a rule in Gmail settings to link all these three to the primary one, meaning I can change my "from" field to be any one of the three and I get all mails from these three into one mailbox. However, I want to detach the non primary from each other and from my Google+.

I used my non-primary email and got reply from someone that informed me he could see:

2 Answers
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By setting up secondary emails so that you can send "from" them, I don't believe you will be able to really break the link that others are seeing between those email addresses and the primary one that is associated with your Google+ account. You are essentially merging aspects of these various email addresses so in a sense they are becoming one identity.

Maybe a better way for you to gather all of your incoming mail in one place would be to setup forwarding from the secondary accounts rather than pulling of the secondary accounts into the primary account. This would not allow you to send "from" those accounts though. If you really need to keep more of a separation of identities (for various aspects of your personal and/or business life), I think you may want to setup an additional primary Gmail account which can be used for the additional identity. Then, for example, any business email addresses can be associated to that secondary identity and any personal email addresses can be associated to the identity you currently have (the one with the Google+ profile that you don't want to advertise so widely).

But something else to consider is that even if you completely break apart your identities, as long as you have a public Google+ profile people will be able to find whatever you have chosen to make public. Maybe you also want to consider making private certain aspects of your Google+ profile?

Specifically, there are settings you can apply for your profile picture's visibility. Please see the Stack Exchange question How does "your Gmail picture" work? for some more details.

I have about 20 email accounts. 5 of them are on Gmail. And I use my one gmail account to read and write emails.

Its very simple, setup your accounts inside your primary gmail account and define your credentials for each of them. setup your signature for each if they belong to different scope of work. I have about 10 signatures.

When you are answering emails, GMail will automatically pick up your email address that you have received email at. And will give you a choice to choose different email address if you want to.

The receving people will still see you sending emails from the email address that they sent emails to (provided you dont change it)